Related papers: BilevelJuMP.jl: Modeling and Solving Bilevel Optim…
Bilevel optimization, a well-established field for modeling hierarchical decision-making problems, has recently intersected with sustainability studies and practices, resulting in a series of works focusing on bilevel optimization problems…
Bilevel optimization is a key framework in hierarchical decision-making, where one problem is embedded within the constraints of another. In this work, we propose a control-theoretic approach to solving bilevel optimization problems. Our…
A bilevel program is an optimization problem whose constraints involve another optimization problem. This paper studies bilevel polynomial programs (BPPs), i.e., all the functions are polynomials. We reformulate BPPs equivalently as…
MLJ (Machine Learing in Julia) is an open source software package providing a common interface for interacting with machine learning models written in Julia and other languages. It provides tools and meta-algorithms for selecting, tuning,…
We present \texttt{MathOptAI.jl}, an open-source Julia library for embedding trained machine learning predictors into a JuMP model. \texttt{MathOptAI.jl} can embed a wide variety of neural networks, decision trees, and Gaussian Processes…
We propose an extended variant of the reformulation and decomposition algorithm for solving a special class of mixed-integer bilevel linear programs (MIBLPs) where continuous and integer variables are involved in both upper- and lower-level…
In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…
Bilevel optimization is a hierarchical framework where an upper-level optimization problem is constrained by a lower-level problem, commonly used in machine learning applications such as hyperparameter optimization. Existing bilevel…
A large number of application problems involve two levels of optimization, where one optimization task is nested inside the other. These problems are known as bilevel optimization problems and have been studied by both classical…
Hyperparameter tuning is an important task of machine learning, which can be formulated as a bilevel program (BLP). However, most existing algorithms are not applicable for BLP with non-smooth lower-level problems. To address this, we…
This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…
Bilevel programs with spatial price equilibrium constraints are strategic models that consider a price competition at the lower level. These models find application in facility location-price models, optimal bidding in power networks, and…
Bilevel optimization has become a powerful framework in various machine learning applications including meta-learning, hyperparameter optimization, and network architecture search. There are generally two classes of bilevel optimization…
Graph theory provides a convenient framework for modeling and solving structured optimization problems. Under this framework, the modeler can arrange/assemble the components of an optimization model (variables, constraints, objective…
Julia is a mature general-purpose programming language, with a large ecosystem of libraries and more than 12000 third-party packages, which specifically targets scientific computing. As a language, Julia is as dynamic, interactive, and…
Bilevel linear programming (LP) is one of the simplest classes of bilevel optimization problems, yet it is known to be NP-hard in general. Specifically, determining whether the optimal objective value of a bilevel LP is at least as good as…
In this article, we propose an interval constraint programming method for globally solving catalog-based categorical optimization problems. It supports catalogs of arbitrary size and properties of arbitrary dimension, and does not require…
In this paper, we consider bilevel optimization problem where the lower-level has coupled constraints, i.e. the constraints depend both on the upper- and lower-level variables. In particular, we consider two settings for the lower-level…
We present NEP-PACK a novel open-source library for the solution of nonlinear eigenvalue problems (NEPs). The package provides a framework to represent NEPs, as well as efficient implementations of many state-of-the-art algorithms. The…
Bilevel programming is one of the very active areas of research with many real-life applications in economics and engineering. Bilevel problems are hierarchical problems consisting of lower-level and upper-level problems, respectively. The…